M.P.
This is a normal toddler way of interacting with her world. Her brain is very under developed. She doesn't have the ability to focus for any length of time.
When you play with her you're in her world. Follow her lead. I suggest that just sitting on the floor with her interacting however is comfortable for her is playing with her. In your world you spend time on one game. She doesn't. It's normal.
Do not feel guilty for not playing with her. She needs your attention, yes, but she doesn't need you constantly playing with her. And......there are other ways to play. You play with her when you change her diaper and sing a song or hand her toys. You play with her when, as my son in law does, pick her up, give her a hug, nuzzle her neck and then put her down when she starts to squirm. Play does not have to be organized. In fact at this age play is not organized.
Gaining a certain amount of independence is a developmental task at this age. Let her be independent when it's reasonable to do so. Letting her move on to a different activity is one of those times.